Question

A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi. Answer:

Answer 1

Answer: The answer is 2,713.

First, find the volume of the hemisphere:

Formula of the hemisphere: V=4/3πr^3

       V=4/3π(9)^3

       V=4/3π(729)

       V=972π

       V=972*3.14

       V=3,052.08/2

       V=1,526.04

Then, find the volume of the cone:

Formula of the cone: V=1/3πr^2h

       V=1/3π(9)^2(14)

       V=1/3π(81)(14)

       V=1/3π(1,134)

       V=378π

       V=378*3.14

       V=1,186.92

Finally, add the volumes: 1,526.04+1,186.92=2,712.96 (Remember, it's important to round!)

The volume of the prop is 2,713.

Answer 2

Volume of cone formula: V = PI x r^2 x h/3

Volume of sphere formula: 4/3 x PI x r^3

Cone: 3.14 x 9^2 x 9/3 = 763.02 cubic inches

1/2 sphere: 1/2 x 4/3 x 3.14 x 9^3 = 1526.04 cubic inches.

Total volume : 1526.04 + 763.02 = 2289.1 cubic inches